CHICAGO (AP) — A former University of Illinois doctoral student on trial for killing a visiting scholar from China searched the internet for instructions on committing murder before the woman vanished, which one expert on serial killers says may be a sign that his boast to have killed 12 other people is false.

Brendt Christensen’s claim, which the FBI hasn’t ruled out, came in conversations recorded by his girlfriend, Terra Bullis, who he may have been trying to impress by saying he was a serial killer. Bullis, the prosecution’s star witness who testified at the federal trial for a second day Thursday, wore an FBI wire over several weeks, once becoming so nervous recording her boyfriend-turned-suspect that she fainted.

Christensen, who is now 29, described to her how he lured Yingying Zhang into his car on June 9, 2017, as she waited for a bus and then forced the 26-year-old into his apartment. There, he raped, choked and stabbed Zhang, then beat her to death with a baseball bat and decapitated her.

“Do you think you might be the next successful serial killer?” Bullis asks him in one conversation. He answers: “I already am.” He calls Zhang victim “No. 13” and says he’s been killing since around 2001 when he was 19.

At a vigil for Zhang on June 29, 2017, Christensen seemed proud as he told Bullis he’d killed others — even tracing “13” on her hand with his finger, she testified Thursday. The FBI arrested him the next day.

Christensen has pleaded not guilty to kidnapping resulting in death, though his lawyer told jurors during opening statements he did kill Zhang. He faces a possible death sentence if convicted.

For someone who purports to be a seasoned killer going back to his days as an undergraduate in physics in Wisconsin, Christensen devoted lots of time researching the topic leading up to Zhang’s disappearance.

He downloaded an article, “Beyond the Grave —Understanding Human Decomposition,” and a paper on “The Criminal Mind of Serial Killers,” and he visited an “abduction 101” fetish forum.

“The contents of Christensen’s internet search history demonstrate his lack of knowledge of basic things that proficient serial killers with high body counts would know,” says Enzo Yaksic, a Boston-based researcher who has studied serial killers for over 15 years.

But Christensen does share some traits with convicted serial killers.

He targeted a stranger, say prosecutors. Sexual fantasies underpinned his desire to kill and he idolized serial killers in history, especially Ted Bundy. A recent study co-authored by Yaksic noted serial killers often share a fondness for violent fictional characters. Christensen’s favorite novel, prosecutors say, was “American Psycho,” about a young professional who kills at night.

A 2015 FBI report on serial killers said 70% percent were highly stressed before they began killing. In 2016, Christensen’s marriage was unraveling. The once straight-A student began getting Fs in all his classes and he abandoned his quest for a Ph.D.

He also shared a longing for infamy, texting two weeks before Zhang went missing that, “I don’t care how I will be remembered, just that I am.”

Choking is also a marker for some serial killers, said Yaksic, because it satisfies their craving for control.

Christensen told Bullis he choked Zhang for 10 minutes.

“She was stronger than any victim I’ve ever had,” he says, adding that some of his victims “were gone in one punch.”

Killers have been known to exaggerate their number of victims, possibly in a bid to become yet more notorious. Before he was executed in 1989, Bundy claimed to have killed 100 women after saying it was 30.

The claims often can’t be proven or disproven, so it’s likely no one will ever be able to say with complete certainty Christensen is lying.

Prosecutors dangled the possibility Christensen killed before during openings last week. Under most circumstances, mention of previous, unproven crimes would lead to a mistrial. But prosecutors seem to want to illustrate, not that Christensen actually killed others, but that homicidal fantasies motivated his killing of Zhang, whose body was never found.

Agent Andrew Huckstadt told jurors this week that the FBI continues to investigate Christensen’s claims. He said that saying they’ve been unable to corroborate them is “not the same as saying it’s completely impossible.”

The investigation likely involves checking if Christensen’s DNA matches DNA found at the scenes of unsolved homicides in Illinois and Wisconsin. He grew up in Stevens Point, Wisconsin, and got his degree at the University of Wisconsin-Madison before moving to the Champaign-Urbana in 2013.

Government filings say there’s evidence of at least one previous assault. They say a woman, referred to as “M.D.,” told the FBI after Christensen’s arrest that she met him for a date in 2013. After meeting for coffee, she says he drove her to a cemetery, choked her and sexually assaulted her.

Defense lawyers say Christensen was in a drunken stupor when he spoke about other victims and that it isn’t true. They’ve also denied M.D.’s allegations.

Actual serial killers, explained Yaksic, demonstrated more patience than Christensen, who only happened upon Zhang and pulled up to her during the day along streets lined with surveillance cameras.